Survival Probabilities of History-Dependent Random Walks
arXiv:cond-mat/0506063 · doi:10.1103/PhysRevE.72.046144
Abstract
We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase-transition occurs when the correlation strength parameter μreaches a critical value μ_c. For strong positive correlations, μ> μ_c, the survival probability is asymptotically finite, whereas for μ< μ_c it decays as a power-law in time (chain length).
3 pages, 2 figures